I think "underground lake" is metaphorical. We have some good geology for our aquifer—it's called the Salt River Valley alluvial basin.[1]
The Phoenix Active Management Area has a bunch of water storage[2]. I'd also direct you to the city's 2021 plan.[3]
[1] https://new.azwater.gov/hydrology/groundwater-modeling/salt-... [2] https://waterbank.az.gov/water-storage [3] https://www.phoenix.gov/waterservicessite/Documents/2021%20C...